C#，数值计算——插值和外推，径向基函数插值（RBF_interp）的计算方法与源程序

1 文本格式

using System;

namespace Legalsoft.Truffer
{
    ///

    /// 径向基函数插值
    /// Object for radial basis function interpolation using n points in dim
    /// dimensions.Call constructor once, then interp as many times as desired.
    ///

    public class RBF_interp
    {
        //public delegateFunc func { get; set; } = null;

        private int dim { get; set; }
        private int n { get; set; }
        private double[,] pts { get; set; }
        private double[] vals { get; set; }
        private double[] w;
        public RBF_fn fn;
        private bool norm { get; set; }

        public RBF_interp(double[,] ptss, double[] valss, RBF_fn func, bool nrbf = false)
        {
            this.dim = ptss.GetLength(1);
            this.n = ptss.GetLength(0);
            this.pts = ptss;
            this.vals = valss;
            this.w = new double[n];
            this.fn = func;
            this.norm = nrbf;

            double[,] rbf = new double[n, n];
            double[] rhs = new double[n];
            for (int i = 0; i < n; i++)
            {
                double sum = 0.0;
                for (int j = 0; j < n; j++)
                {
                    //sum += (rbf[i, j] = fn.rbf(rad(pts[i, 0], pts[j, 0])));
                    double r = Globals.dist(Globals.CopyFrom(i, pts), Globals.CopyFrom(j, pts));
                    rbf[i, j] = func.rbf(r);
                    sum += rbf[i, j];
                }
                if (norm)
                {
                    rhs[i] = sum * vals[i];
                }
                else
                {
                    rhs[i] = vals[i];
                }
            }
            LUdcmp lu = new LUdcmp(rbf);
            lu.solve( rhs,  w);
        }

        public double interp(double[] pt)
        {
            double fval;
            double sum = 0.0;
            double sumw = 0.0;
            if (pt.Length != dim)
            {
                throw new Exception("RBF_interp bad pt size");
            }
            for (int i = 0; i < n; i++)
            {
                //fval = fn.rbf(rad(pt[0], pts[i, 0]));
                fval = fn.rbf(Globals.dist(pt, Globals.CopyFrom(i, pts)));
                sumw += w[i] * fval;
                sum += fval;
            }
            return norm ? sumw / sum : sumw;
        }
        /*
        public double rad(double[] p1, double[] p2)
        {
            double sum = 0.0;
            for (int i = 0; i < dim; i++)
            {
                sum += Globals.SQR(p1[i] - p2[i]);
            }
            if (sum <= float.Epsilon)
            {
                return 0.0;
            }
            return Math.Sqrt(sum);
        }
        */
    }
}
 

2 代码格式

using System;

namespace Legalsoft.Truffer
{
    /// 

    /// 径向基函数插值
    /// Object for radial basis function interpolation using n points in dim
    /// dimensions.Call constructor once, then interp as many times as desired.
    /// 
    public class RBF_interp
    {
        //public delegateFunc func { get; set; } = null;

        private int dim { get; set; }
        private int n { get; set; }
        private double[,] pts { get; set; }
        private double[] vals { get; set; }
        private double[] w;
        public RBF_fn fn;
        private bool norm { get; set; }

        public RBF_interp(double[,] ptss, double[] valss, RBF_fn func, bool nrbf = false)
        {
            this.dim = ptss.GetLength(1);
            this.n = ptss.GetLength(0);
            this.pts = ptss;
            this.vals = valss;
            this.w = new double[n];
            this.fn = func;
            this.norm = nrbf;

            double[,] rbf = new double[n, n];
            double[] rhs = new double[n];
            for (int i = 0; i < n; i++)
            {
                double sum = 0.0;
                for (int j = 0; j < n; j++)
                {
                    //sum += (rbf[i, j] = fn.rbf(rad(pts[i, 0], pts[j, 0])));
                    double r = Globals.dist(Globals.CopyFrom(i, pts), Globals.CopyFrom(j, pts));
                    rbf[i, j] = func.rbf(r);
                    sum += rbf[i, j];
                }
                if (norm)
                {
                    rhs[i] = sum * vals[i];
                }
                else
                {
                    rhs[i] = vals[i];
                }
            }
            LUdcmp lu = new LUdcmp(rbf);
            lu.solve( rhs,  w);
        }

        public double interp(double[] pt)
        {
            double fval;
            double sum = 0.0;
            double sumw = 0.0;
            if (pt.Length != dim)
            {
                throw new Exception("RBF_interp bad pt size");
            }
            for (int i = 0; i < n; i++)
            {
                //fval = fn.rbf(rad(pt[0], pts[i, 0]));
                fval = fn.rbf(Globals.dist(pt, Globals.CopyFrom(i, pts)));
                sumw += w[i] * fval;
                sum += fval;
            }
            return norm ? sumw / sum : sumw;
        }
        /*
        public double rad(double[] p1, double[] p2)
        {
            double sum = 0.0;
            for (int i = 0; i < dim; i++)
            {
                sum += Globals.SQR(p1[i] - p2[i]);
            }
            if (sum <= float.Epsilon)
            {
                return 0.0;
            }
            return Math.Sqrt(sum);
        }
        */
    }
}